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  • 1
    Electronic Resource
    Electronic Resource
    Function-space quasi-Newton algorithms for optimal control problems with bounded controls and singular arcs (1976)
    Springer
    Journal of optimization theory and applications 20 (1976), S. 455-479 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; numerical methods ; computing methods ; gradient methods ; quasi-Newton algorithms ; bounded control problems ; singular arcs
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Two existing function-space quasi-Newton algorithms, the Davidon algorithm and the projected gradient algorithm, are modified so that they may handle directly control-variable inequality constraints. A third quasi-Newton-type algorithm, developed by Broyden, is extended to optimal control problems. The Broyden algorithm is further modified so that it may handle directly control-variable inequality constraints. From a computational viewpoint, dyadic operator implementation of quasi-Newton methods is shown to be superior to the integral kernel representation. The quasi-Newton methods, along with the steepest descent method and two conjugate gradient algorithms, are simulated on three relatively simple (yet representative) bounded control problems, two of which possess singular subarcs. Overall, the Broyden algorithm was found to be superior. The most notable result of the simulations was the clear superiority of the Broyden and Davidon algorithms in producing a sharp singular control subarc.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00933131
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    Paper (German National Licenses)
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  • 2
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    Function-space quasi-Newton algorithms for optimal control problems with bounded controls and singular arcs (1976)
    Springer
    Details
    Publication Date: 1976-12-01
    Print ISSN: 0022-3239
    Electronic ISSN: 1573-2878
    Topics: Mathematics
    Published by Springer
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    PAPER CURRENT
  • 3
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    Function-space quasi-Newton algorithms for optimal control problems with bounded controls and singular arcs (1976)
    In:  Other Sources
    Details
    Publication Date: 2019-06-27
    Description: Two existing function-space quasi-Newton algorithms, the Davidon algorithm and the projected gradient algorithm, are modified so that they may handle directly control-variable inequality constraints. A third quasi-Newton-type algorithm, developed by Broyden, is extended to optimal control problems. The Broyden algorithm is further modified so that it may handle directly control-variable inequality constraints. From a computational viewpoint, dyadic operator implementation of quasi-Newton methods is shown to be superior to the integral kernel representation. The quasi-Newton methods, along with the steepest descent method and two conjugate gradient algorithms, are simulated on three relatively simple (yet representative) bounded control problems, two of which possess singular subarcs. Overall, the Broyden algorithm was found to be superior. The most notable result of the simulations was the clear superiority of the Broyden and Davidon algorithms in producing a sharp singular control subarc.
    Keywords: CYBERNETICS
    Type: Journal of Optimization Theory and Applications; 20; Dec. 197
    Format: text
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    NASA TECHNICAL REPORTS
  • 4
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    Shuttle ascent trajectory optimization with function space quasi-Newton techniques (1974)
    In:  Other Sources
    Details
    Publication Date: 2019-07-13
    Description: A Space Shuttle ascent trajectory optimization problem from lift-off to orbital insertion is solved with a function space version of a quasi-Newton parameter optimization method developed by Broyden. The problem includes five parameter and one bounded-function controls, two state-variable constraints, and four terminal conditions. The bounded controls are treated directly, while the remaining constraints are adjoined to the performance index (maximum payload) with penalty functions. The problem is formulated as a four-phase variational problem (liftoff, pitch-over, gravity-turn, linear tangent steering), and the appropriate gradients are developed by first variation theory. A projection operator is introduced to aid in the interpretation of the algorithm with mixed parameter and function controls.
    Keywords: SPACE SCIENCES
    Type: AIAA PAPER 74-824 , Mechanics and Control of Flight Conference; Aug 05, 1974 - Aug 09, 1974; Anaheim, CA
    Format: text
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    NASA TECHNICAL REPORTS
  • 5
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    Techniques for shuttle trajectory optimization (1973)
    In:  CASI
    Details
    Publication Date: 2019-06-27
    Description: The application of recently developed function-space Davidon-type techniques to the shuttle ascent trajectory optimization problem is discussed along with an investigation of the recently developed PRAXIS algorithm for parameter optimization. At the outset of this analysis, the major deficiency of the function-space algorithms was their potential storage problems. Since most previous analyses of the methods were with relatively low-dimension problems, no storage problems were encountered. However, in shuttle trajectory optimization, storage is a problem, and this problem was handled efficiently. Topics discussed include: the shuttle ascent model and the development of the particular optimization equations; the function-space algorithms; the operation of the algorithm and typical simulations; variable final-time problem considerations; and a modification of Powell's algorithm.
    Keywords: SPACE SCIENCES
    Type: NASA-CR-134169 , REPT-011482-F
    Format: application/pdf
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    NASA TECHNICAL REPORTS
  • 6
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    Function space quasi-Newton algorithms for optimal control problems with bounded controls and singular arcs (1973)
    In:  Other Sources
    Details
    Publication Date: 2019-07-13
    Description: Two existing function space algorithms, Davidon and projected gradient, are modified so that they may handle directly control variable inequality constraints. A third quasi-Newton type algorithm developed by C. G. Broyden is extended to optimal control problems. The Broyden algorithm is further modified so that it also may handle directly control variable inequality constraints. These methods along with a pure gradient and two conjugate gradient algorithms are simulated on three relatively simple yet representative bounded control problems, two of which have singular subarcs. Overall the Broyden algorithm was found to be superior. The most notable result of the study was the clear superiority of the Broyden and Davidon algorithms in producing a sharp interior control subarc.
    Keywords: MATHEMATICS
    Type: AAS PAPER 73-240 , Astrodynamics Conference; Jul 16, 1973 - Jul 18, 1973; Vail, CO; US
    Format: text
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    NASA TECHNICAL REPORTS
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